Individual competitions are between individuals. 

Team competitions are between Groups (or in the case of Program to Program competitions, between entirely different companies/locations/etc). In order to start a team competition, you have to be the administrator of a group. 

If you're running a team competition on Averages, people who do not enter a step entry weigh against the team average -- thus it's vital that you have as high a participation in your team as possible.

Another point worth mentioning is that with all competitions, data in competitions is only tabulated between the competition dates. However team/group data is tabulated in an ongoing manner, no matter if that team is in a competition or not. This data does not weigh against the competition if it's outside of the competition's dates, however.